A278333 a(n) = A278332(n+1)/(n+1) for n>=0.

1, 1, 3, 22, 181, 2111, 31471, 563305, 11634169, 275850685

Offset: 0

Author

Paul D. Hanna, Nov 18 2016

Keywords

• nonn
• more

Comments

E.g.f. of A278332 equals the limit of the average of all permutations of the compositions of the functions x*exp(x^k), for k=1..n, as n increases.

Examples

			E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 181*x^4/4! + 2111*x^5/5! + 31471*x^6/6! + 563305*x^7/7! + 11634169*x^8/8! + 275850685*x^9/9! +...
RELATED SERIES.
log(A(x)) = x + 2*x^2/2! + 15*x^3/3! + 96*x^4/4! + 1100*x^5/5! + 15870*x^6/6! + 278817*x^7/7! + 5558616*x^8/8! + 129258684*x^9/9! +...
		

Crossrefs

Cf. A278332.